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Properties

Label 1386.2.w
Level $1386$
Weight $2$
Character orbit 1386.w
Rep. character $\chi_{1386}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 592 160 432
Cusp forms 560 160 400
Eisenstein series 32 0 32

Trace form

\( 160 q - 160 q^{4} - 4 q^{7} - 8 q^{9} + O(q^{10}) \) \( 160 q - 160 q^{4} - 4 q^{7} - 8 q^{9} - 12 q^{13} + 12 q^{14} + 28 q^{15} + 160 q^{16} + 36 q^{17} + 8 q^{18} + 4 q^{21} - 24 q^{23} - 80 q^{25} - 36 q^{27} + 4 q^{28} - 12 q^{29} + 8 q^{36} + 4 q^{37} + 4 q^{39} + 12 q^{41} + 4 q^{43} + 12 q^{45} - 12 q^{46} + 72 q^{47} + 16 q^{49} - 24 q^{50} - 8 q^{51} + 12 q^{52} + 48 q^{53} - 36 q^{54} - 12 q^{56} - 16 q^{57} - 28 q^{60} - 72 q^{62} - 92 q^{63} - 160 q^{64} + 56 q^{67} - 36 q^{68} + 84 q^{69} + 24 q^{70} - 8 q^{72} - 36 q^{74} + 36 q^{75} + 8 q^{79} + 40 q^{81} - 4 q^{84} - 24 q^{86} + 36 q^{87} - 12 q^{89} - 36 q^{90} + 24 q^{91} + 24 q^{92} + 56 q^{93} - 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)